The modern airplane design works well, but from a fuel efficiency standpoint, could planes be designed more aerodynamically to lower drag and increase lift?

Scientists felt they could in theory, but they lacked experimental evidence. They started with a configuration where the entire plane is one big wing. Then they added a body designed to minimize drag and, most critically, a small tail, which essentially serves to undo aerodynamic disturbances created by the body. They analyzed the airflows and at various relative angles for the wings, body and tail, searching for ways to achieve greater lift (the better for carrying cargo) and lower drag (for higher fuel efficiency).

The flying wings alone provide an ideal (but impractical) baseline, since it's hard to carry people or cargo in such a shape. The presence of a body immediately lowers the lift and increases the drag. The addition of just the right kind of tail, however, can restore the lift, and reduce the drag, occasionally to nearly wing-only levels. The most important point is that this model resembles bird like structure.

It isn't yet possible to duplicate a bird's aerodynamics which was created by Allah. The reason we can't now and may never make a plane like a bird is because the bird instantly changes its shape as it flies. A plane can't do that and the parts that do move are hard to make move. A bird doesn't use ailerons; it moves its entire wing when gliding.

The way Allah creates is the most beautiful, the most efficient and logical one. It is possible to see in all aspects of life. In this century even with our technology and knowledge, we can’t really imitate the living creatures’ features. Also Allah shows these features to inspire us as examples to simplify our life. There are many inventions come to life in this way.

Have they not looked at the birds above them, with wings outspread and folded back? Nothing holds them up but the All-Merciful. He sees all things. (Surat al-Mulk, 19)

Do you not see that everyone in the heavens and earth glorifies Allah, as do the birds with their outspread wings? Each one knows its prayer and glorification. Allah knows what they do. (Surat an-Nur, 41)